Stationary concentrating collectors provide a modest amount of concentration without the necessity for tracking the sun. Examples of concentrating collectors are those employing some variation of the compound-parabolic – concentrator (CPC) reflector system invented by R. Winston at The University of Chicago and developed by ANL and The University of Chicago. Other nonimaging optical systems are also included in this category. Most frequently, these collectors use an evacuated tube as the receiver, so they are often referred to as "evacuated-tube" collectors (ETCs). It is really the optical response of the stationary concentrators that distinguishes them from flat-plate evacuated collectors, described in the preceding section.
In their present state of development, concentrating ETCs are capable of delivering energy at temperatures of up to about 150°C with reasonable efficiency. Today’s collectors normally weigh 30 to 40 kg/m^ and cost about $200-250 (U. S.)/m^ at the manufacturer’s site. The cost of the installed
collector array may be $400-550 (U. S.)/m. The current generation of concentrating ETCs uses aluminum or aluminized plastic reflectors, uncoated glass tubes, and multilayer selective coatings that have rather low emissivities (-0.05) but also exhibit rather poor absorption (<0.80). Recent advances in the optical design of nonimaging concentrators^* have not yet been exploited in commercial designs. For these reasons, it was the consensus of a special workshop on evacuated-coilector technology sponsored by the DOE in 1979 that the optical efficiency of concentrating evacuated collectors could probably be improved by 50%. Present evacuated collectors are also known to have high manifold heat losses — frequently the manifold losses equal the combined radiation and conduction losses from the tubes. The workshop participants estimated that the overall loss coefficient Ul could be reduced by 25%. Thus, the technology of concentrating evacuated collectors, unlike that of FPCs, is immature and has considerable potential for performance improvement.
In our initial attempts to model the thermal performance of evacuated collectors, the potential for improvement was taken into account by considering two models, one representing a state-of-the-art commercial collector and the other representing an advanced collector (defined as a collector with a 50% greater efficiency and a 25% lower U^). Since the proposal of this hypothetical collector, experimental results from an advanced prototype collector under development by R. Winston’s group at The University
of Chicago have confirmed that the assumed level of performance is possible and perhaps even conservative.22-24 new еоцее^ог employs a shaped
vacuum tube in which the reflective surface is deposited on the inside. (This means that silver can be used to enhance the reflectivity.) A metallic receiver is used so that the higher-performance selective coatings can be applied, and the geometry of the tube employs the most advanced optical design. The net result is a collector that matches or exceeds the performance of a high-quality parabolic trough at temperatures up to about 300°C and requires no tracking or seasonal adjustment. Although the integrated CPC collector is still far from being a marketable product, its development (coupled with other advances reported in the private sector) justifies inclusion of an advanced evacuated collector in our study.
Thermal-efficiency curves for typical conventional and advanced stationary concentrating collectors, determined using equations in this section, are shown in Fig. 2.3; a curve for a typical commercial parabolic trough is included for comparison. The expected characteristics of the advanced collector are based on laboratory measurements.
The modeling equations for a stationary concentrator with an evacuated receiver are similar to those for FPCs, except for the optical efficiency. The
Fig. 2.3 Instantaneous Efficiency Curves for Typical Stationary and Tracking Solar Collectors
concentrating optics exhibit a complex response to the orientation of the sun and generally use only a fraction of the diffuse radiation. Details concerning a description of the angular response of CPCs and other optical systems are available in the literature. The response to the beam radiation can generally be approximated by the product of two incident-angle modifying factors: one (KaT, NS) related to the projection of the angle of incidence onto a plane normal to the collector and passing through the sun — i. e., the N-S plane; and one (KaT, EW) related to the projection of the angle of incidence onto a plane orthogonal to the plane of the collector and the N-S plane. If the axis of the tube and reflector syste m lies in the N-S plane, the usual configuration for drainable Owens-Illinois* (OI) and SUNMASTER  collectors, the angular response to changes in projection of the incident angle on the N-S plane is adequately described by Eq. 3. The angular response to changes in the transverse direction, E-W, is much more complex and depends upon the design of the reflector. Examples of measured incident-angle modifiers for the transverse-plane angle for several collectors are shown in Fig. 2.4. The measured response of the SUNMASTER collector has been verified by detailed ray-trace calculations by Mclntire,^ whereas the measurements on the various reflector systems of the OI and General Electric* (GE) collectors do not match the calculations as well. Partly for this reason, we have chosen a model based on the SUNMASTER reflector system. The angular-response curve increases substantially for the first 35 degrees; this is important in calculating the total energy collected in a day.
The specific equations used for the study are:
I = I, cos0 + 1,(0 /2тт) a b d c
П, – п ГГГк, NS * К, EW)(cos0 d о J J 4 ат ‘4"‘
where the integrals are carried out over the acceptance angle of this collector, 0C. For the SUNMASTER collector, Eq. 12 reduces to the following:
Fig. 2.4 Incident-Angle Modifiers for Several Commercial Stationary Concentrating Collectors
nd  0.71 n0 (13)
The parameters (based on gross area) used for the commercial and advanced collectors are given in Table 2.1.